I will discuss results on quasisymmetric rigidity of Julia sets of certain rational functions. One such result states that if f is a postcritically nite rational map whose Julia set J (f) is a Sierpinski carpet, then every quasisymmetric map of J (f) onto itself is the restriction to J (f) of a Mobius transformation. This is joint work with Mario Bonk and Misha Lyubich.
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